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The HCF of two numbers is 7 and their LCM is 434. If one of the numbers is 14, the other number is:
146
48
217
52
217
Use the property that the product of two numbers equals the product of their LCM and HCF. Divide the product (7 × 434) by 14: (7 × 434) / 14 = 434 / 2 = 217.
HCF = 7, LCM = 434, One number = 14
LCM×HCF=First Number×Second Number
Use the property that the product of two numbers equals the product of their LCM and HCF. Divide the product (7 × 434) by 14: (7 × 434) / 14 = 434 / 2 = 217.
Confusing the product of LCM and HCF with the sum, or incorrectly performing the division by 14 instead of using the factor 7.
State the relationship
The fundamental property of two numbers is that the product of the Highest Common Factor (HCF) and the Least Common Multiple (LCM) is equal to the product of the two numbers.
LCM×HCF=a×b
Substitute given values
Substitute the given values HCF=7, LCM=434, and a=14 into the formula to solve for the unknown number b.
434×7=14×b
Solve for the unknown number
Isolate b by dividing both sides by 14. We can simplify this as b=(434×7)/14. Since 14=7×2, this becomes 434/2.
b=14434×7=2434=217
C is correct because calculating the product of the HCF and LCM divided by the first number results in 217.
This property (Product of two numbers = HCF × LCM) is specific to two numbers. For three numbers, the product is NOT simply HCF × LCM; always verify the number of variables before applying.
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